The most common failure of a MagSafe power adapter is when the insulation around the chord, through repeated movement and stress, breaks and exposes the wire inside, which, in turn breaks and then you have a useless charger and apple want you to shell out £65 for a new one. The main wire that breaks is the shielding wire around the main core, this is a major design floor or maybe Apple designed it this way so you had to buy a new one every year? Anyway this is really a simple fix that costs under £4 (nothing if you already have everything), this fix works for all adapters and you don't have to open up the transformer and takes around 10 minutes to do. As an added bonus it makes the wires stronger so they wont break again, it a one time fix.
WARNING! - UNPLUG YOUR POWER SUPPLY BEFORE DOING THIS YOU COULD RISK DAMAGE TO YOUR CHARGER OR TO YOURSELF I CANNOT BE HELD RESPONSIBLE FOR ANY INJURIES YOU SUSTAIN THROUGH ELECTROCUTION
What you'll need:
A broken charger (thats a given)
First off you need to remove some insulation around the area with your x-acto you can remove as much as you fell is necessary but you need enough to be able to solder it so 5mm either side should do you then want to twist each end of the wire so its a nice bundle and then tin, this also makes that area stronger so it is less likely to break again. if you don't know what tinning is her is an excellent guide. http://www.mediacollege.com/misc/solder/tinning.html